A Method for Avoiding Numerical Instability in FDTD-based Surge Simulations and its Application to Representation of Thin Wires

Abstract

The FDTD (Finite Difference Time Domain) method, which is used for the computation of electromagnetic fields, is a useful tool for surge problems in three-dimensional arrangements, which cannot be rigorously treated by simulation methods such as EMTP (Electromagnetic Transients Programs) based on circuit theory.In the FDTD method, thin wires such as power lines are often represented by forcing the electric fields along the wires to zero. If a thin wire is represented in this way, its radius is determined by the size of the cells surrounding the wire. Although the technique for simulating an arbitrary radius has already been proposed, numerical instability often occurs in simulations when the wire radius is much smaller than the size of the cells surrounding the wire. As a conventional countermeasure against such numerical instability, the time discretization is often set to a smaller value than that based on Courant's condition. However, the smaller time discretization results in an increase in the calculation time.We propose a new technique for avoiding the numerical instability. Using this technique, in only a part of an analysis space where the numerical instability may occur, the time discretization is set to a value smaller than that based on Courant's condition, while the time discretization is set to a value close to that based on Courant's condition in the other part of the analysis space. We performed an FDTD-based simulation of a thin wire using the proposed numerical stabilization technique for validation.